The present invention relates generally to single carrier and multi-carrier communication systems, and particularly to reducing Peak to Average power Ratios (“PAR”) in such systems.
Multi-carrier transmission systems have evolved out of a need to provide increased transmission rates for information via existing communication channels. In its broadest aspect, multi-carrier systems transmit a number of independent signals on a common channel. Each modulated signal is centered on a different frequency, the frequencies being normally equally spaced within a predetermined transmission bandwidth of the channel. These frequencies are commonly termed carrier frequencies.
Transmission channels are fundamentally analog and thus may exhibit a variety of transmission effects. In particular, telephone lines, as for example Digital Subscriber Line (DSL) Systems (DSLs) use some form of modulation.
A transmitter system normally converts each successive group of b bits from a digital bit stream into one of 2b data symbols xm via a mapping (generally one-to-one) using an encoder. Each group of b bits constitutes a message m, with M=2b possible values. The data symbols are N-dimensional vectors xm and the set of M vectors form a signal constellation. Modulation is the process of converting each successive data symbol vector into a continuous-time analog signal xm(t) that represents the message corresponding to each successive group of b bits.
A particular implementation of a multi-carrier system is a Discrete Multi-Tone (DMT) scheme that partitions the available transmission bandwidth into many narrow-band subchannels over which parallel data streams are modulated. The DMT technique has been adopted for use in Asymmetric Digital Subscriber Line (ADSL) technology. In ADSL, DMT is used to generate 224 separate subchannels (that is “tones”) that are 4.3125 kHz wide and that are located between 138 kHz to 1.104 MHz for downstream transmission to an end user, and 26 separate subchannels that are located between 26 kHz to 138 kHz for upstream transmission from the end user.
FIG. 1 illustrates a typical DMT transmitter 10. The transmitter incorporates several components including an encoder 102 and a discrete multi-tone modulator 104. The encoder 102 segments the incoming bit streams and encodes it such that it can be transmitted over several different carriers N. The encoder 102 outputs data sequences for the N channels. Modulator 104 modulates the segmented data inputs using an appropriate modulation scheme such as QAM. These inputs are complex inputs that are passed to a discrete multi-tone modulator. The output of the modulator 104 provides the DMT vector of constellation points X comprised of the individual channel subsymbols. An Inverse Fourier Transformer (IFFT) 106 transforms X to provide a discrete time equivalent by any suitable algorithm. The IFFT 106 is used for converting the frequency domain vector X to the time domain vector x. After the encoded signal has been modulated to form a discrete multi-tone signal, a cyclic prefix is appended 108 to the discrete multi-tone encoded signal. The cyclic prefix is used primarily to simplify the demodulation of the discrete multi-tone signals. The cyclic prefix is a replica of the last several samples of the digital signal and is required for DMT transmissions to mitigate inter-symbol interference. The transmitter 10 also includes a series of digital filters 110, Digital to Analog Converter (DAC) 112, analog filters 114 and a line driver 116.
The discrete time signal is passed through the digital filter 110 before being processed by the DAC 112. The DAC 112 converts the discrete time signal into a continuous time signal. The continuous time signal is applied via the analog filters 114, to the line driver 116. The line driver 116 drives the signal onto the communication line 118, which may take the form of a twisted pair phone line. The discrete multi-tone encoded signal with its cyclic prefix is then transmitted over the communication line to a remote location (not shown).
The transmission capability of the individual channels is evaluated for each connection, and data is allocated to the subchannels according to their transmission capabilities (the number of bits each channel can support). The bit distribution is determined adaptively in discrete multi-tone systems. To facilitate this, the transmitter also includes a line monitor (not shown) that monitors the communication line to determine the line quality of each of the available subchannels. The determination of what subchannels to transmit the encoded data over as well as how much data to transmit over each subchannel is dynamically determined on the basis of several factors. The factors include the detected line quality parameters, subchannel gain parameters, a permissible power mask, and the desired maximum subcarrier bit-error rates. Subchannels that are not capable of supporting data transmission are not used, whereas the bit-carrying capacity of subchannels that can support transmission is maximized. Thus, by using DMT in an ADSL system, the transmission capability of each twisted pair connection is maximized.
As mentioned with reference to FIG. 1, summing the modulated carriers creates a DMT symbol. Summing many random modulated carriers leads to a transmitted signal whose power probability density function is very close to Gaussian. In other words if viewed in the time domain as one-dimensional signals, the probability distribution of multichannel signals approaches a Gaussian distribution. Thus the DMT symbol has a much higher Peak-to-Average power Ratio (PAR) than most single carrier signals. A clip is defined to occur when the transmit signal sample exceeds the maximum implemented value for the transmitter (often set by the DACs maximum value) or a predetermined threshold. For example, for a clipping probability of 10-7, the PAR of a Gaussian signal is approximately 5.33 (or 14.5 dB) as opposed to 2.45 (or 7.8 dB) for a single carrier. Therefore, in order to minimize clipping of the DMT signal, DMT systems must use a Digital to Analog Converter (DAC) with high resolution and an Analog Front End (AFE) with a large dynamic range. Since the AFE can constitute a significant percentage of the cost of the system as well as the power drainage of the system, it is desirable to reduce the PAR of the signal at these components for reducing their requirements and saving power.
Many PAR reduction methods have been proposed as exemplified in U.S. Pat. No. 5,623,513, U.S. Pat. No. 5,787,113, U.S. Pat. No. 5,768,318, U.S. Pat. No. 5,835,536, and in a document by J. Tellado, J. Cioffi, entitled “Further Results on Peak-to-Average Ratio Reduction”, ANSI contribution T1E1.4/98-252, August 1998. The methods disclosed therein modify the DMT transmitter in such way that the PAR of the signal immediately output from the modulator 104 is reduced. PAR reduction ranging between 2 and 6 dB from the 14.5 dB figure has been achieved in these systems.
Another method of achieving PAR reduction is described in “PAR Reduction in Multicarrier Transmission Systems”, ANSI contribution T1E1.4/97-367, December 1997 and in PCT Application No. PCT/US99/08682. This method consists of adding a waveform, or peak reducing kernels, to the DMT symbol such that the peak of the kernel cancels the peaks of the signal. In FIG. 3, a block diagram of an implementation of the peak reducing kernel method is illustrated generally by the numeral 30. Selection of the peak reduction frequencies is made in advance. Generally those frequencies in the channel that have a lot of noise and are capable of only carrying low bit rate signals are used as peak reduction frequencies. The particular kernel is also computed beforehand based upon the selection of the peak reduction frequencies. A scaled and cyclically shifted replica of the kernel is added to the output of the modulated signal, x(n), to cancel its largest peak. This procedure is repeated for the next largest peak and continues for a fixed number of iterations or until all the peaks larger than a given threshold has been reduced. Therefore, the final waveform of the kernel added to the signal x(n) is of the form:       ∑    i    ⁢            A      i        ⁢                  (                  k          ⁢                      (                          n              -                              n                i                                      )                          )                    modulo        ⁢                                   ⁢        N            where Ai is the amplitude of the ith element, ni is the phase shift of the ith element, and N is the DMT symbol size. Thus the scaled and delayed kernel is added to x resulting in xclip=x+k, where k is a linear combination of one ore more kernels that that have been scaled and time delayed to negate one or more peaks in x.
Since the kernel is not necessarily zero outside of its peak, a signal peak that has been reduced below a threshold may rise above the threshold while reducing other signal peaks. Therefore, the kernel, k(n), is chosen to be impulse-like for minimizing the probability of regenerating peaks.
Furthermore, in order not to interfere with the data transmission, the kernel is chosen such that in the frequency domain, it is orthogonal to the data carriers and satisfies the property:Xk·Kk=0where Xk is signal in the frequency domain and Kk is the kernel in the frequency domain. In other words, the kernel is zero in data carrying carriers and no data is transported in carriers reserved for the kernel. FIGS. 2(a) and (b) show the relationship between X and K in the frequency domain. In practice, only a small percentage of the available carriers need to be reserved for the kernel, thereby causing only a small reduction in data rate.
Although the above techniques are successful in reducing the PAR, it has been recognized by J. Tellado and J. Cioffi, in ANSI contribution T1E1.4/98-252, August 1998 entitled “Further Results on Peak-to-Average Ratio Reduction,” that the digital filters 110 and analog filters 114 regenerate the PAR that was reduced at the output of the IFFT 106 and leads to negligible benefits at the DAC 112 or line driver 116. Since the transmit filters (digital 110 and/or analog 114) are essential for meeting the transmission Power Spectral Density (PSD) mask, they cannot be eliminated to avoid PAR losses.
Referring to FIG. 3, there is a block diagram of a transmitter including a PAR reducer. This transmitter uses peak reducing kernels according to a known technique. The transmitter 30 includes a encoder 102 and modulator 104, an IFFT 106, a PAR reducer 302, cyclic prefix insertion module 108, digital filters 110, DAC 112, analog filters 114 and line drivers 116. Modulator 104 provides a frequency domain signal X to the IFFT 106. The IFFT 106 applies an inverse Fourier transform to X to produce a discrete time signal x(n). In the case of DMT a discrete time signal x is generated from a number of complex valued QAM modulated signals, which are the components of X. Each element of x(n) is a symbol derived from X defined by:             x      ⁡              (        n        )              =                  1                  N                    ⁢                        ∑                      k            =            0                                N            -            1                          ⁢                              X            k                    ⁢                      ⅇ                          j              ⁢                                                           ⁢              2              ⁢                                                           ⁢              π              ⁢                                                           ⁢                              kn                /                N                                                          ,      k    =    0    ,            …      ⁢                           ⁢      N        -    1  which can be written as x=QX where Q is the IFFT matrix and the elements of Q are       q          n      ,      k        =            1              N              ⁢          ⅇ                        j          ⁢          2                ⁢                                   ⁢        π        ⁢                                   ⁢                  kn          /          N                    where:                N is the number of channels or tones;        X is the DMT vector of constellation points mapped from the m-th block of encoded bits;        x is the time vector transformed from X by the IFFT; and        n is a discrete time indexing and denotes Nyquist Rate samples.        
The PAR reducer 302 performs a PAR reduction on x(n) by applying peak reducing kernels to x(n). More specifically, the PAR reducer 302 adds peak reduction signals k to x(n) in order to reduce the PAR of x(n). Selection of the peak reduction frequencies is made in advance. Generally those frequencies in the channel that have a great deal of noise and are capable of only carrying low bit rate signals are used as peak reduction frequencies. The particular kernel may also be computed beforehand based upon the selection of the peak reduction frequencies. It is assumed that the receiver is informed of which frequencies are peak reduction frequencies. This information may be transmitted to the receiver just before a new set of peak reduction frequencies is used.
The values of the peak reduction signals may be represented as a vector c in the time domain and the vector C in the frequency domain. Thusx+c=Q(X+C)and the possible values of c are chosen to reduce the PAR in the signal x. The time domain signal generated by the vector x+c is then the desired PAR reduced signal.
As mentioned above, the peaks in the time domain signal x(t) can be scaled by adding or subtracting an appropriately scaled impulse function at those peak time values. The impulse function is normally constructed from the selected peak reduction frequencies and can be used to create the approximate impulse function k(t) or kernel. Since K has non-zero values only at the peak reduction frequencies, C may be represented as a linear combination of K. The linear combinations of K correspond to the scaled and shifted versions of the kernel k such that scaled and shifted versions of k negate the peaks of x.
A scaled and cyclically shifted replica of the kernel is added to the output of the modulated signal x(n) to cancel its largest peak. If only one peak is minimized during a single iteration of applying the kernel k then y=x+Aik(n−ni)modN in the discrete time domain, where A is a scaling factor and n, is a time shift. This procedure is repeated for the next largest peak and continues for a fixed number of iterations or until all the peaks larger than a given threshold have been reduced. Therefore, the final waveform of the kernel added to the signal x(n) is of the form:       ∑    i    ⁢            A      i        ⁢                  (                  k          ⁢                      (                          n              -                              n                i                                      )                          )            modN      where Ai is the amplitude of the ith element, ni is the phase shift of the ith element, and N is the DMT symbol size. Once the PAR reducer 302 has finished reducing the peak to average power ratio of the signal x, it provides x as another symbol of the discrete time sequence y(n) to the cyclic prefix block 108 where       y    ⁢          (      n      )        =            x      ⁢              (        n        )              +                  ∑        i            ⁢                        A          i                ⁢                                            (                              k                ⁢                                  (                                      n                    -                                          n                      i                                                        )                                            )                        modN                    .                    
The sequence y(n) is filtered by digital filter 110, to produce a sequence w(n)=y(n){circumflex over (x)}h(n) where {circumflex over (x)} denotes convolution and h(n) is the response of the digital filter, before being passed through to DAC 112 and the filter 114 to get the continuous time signal for transmission. (A detailed description of this process is described in PCT Application No. PCT/US99/08682.)
The above scheme does not take into consideration the effect of the filters 110 and 114 in reducing the PAR. Accordingly, there is needed a PAR reduction mechanism capable of addressing the effect of the digital and analog filters to reduce the PAR after filtering at various points in the transmitter.